Systems and methods for fine-tuning refractive surgery

ABSTRACT

Systems and methods for fine-tuning refractive shapes for vision treatment are provided. Techniques encompass determining a variable index of refraction for a cornea of the eye, and determining the refractive treatment shape for the eye based on the variable index of refraction. Techniques also encompass determining a variable radius of curvature of an anterior surface of a cornea of the eye, and determining the refractive treatment shape for the eye based on the variable radius of curvature.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a nonprovisional of, and claims the benefit ofpriority to, U.S. Provisional Patent Application No. 60/953,425 filedAug. 1, 2007, which is incorporated herein by reference for allpurposes.

BACKGROUND OF THE INVENTION

Embodiments of the present invention relate the field of visiontreatment, and in particular to systems and methods for fine-tuningablation profiles and other treatment shapes.

Many current laser correction techniques are based on a nominal valuethat reflects a constant index of refraction of the corneal stroma.These techniques do not consider the variation that may exist in therefractive index of the conical stroma. Known techniques are often basedon a nominal value, which may be 1.376, for example. Moreover, manycurrent approaches are based on or employ a nominal value that reflectsa constant radius of curvature of the anterior surface of the cornea.This can cause up to about a 2% to 3% error in ablation depth, forexample.

However, such estimations may not accurately represent the actualanatomy of the ocular system, or changes that may occur in the anatomyor the ablation process as the ablation process is carried out. Hencethere is a need for systems and methods that consider a variation in therefractive index, which more closely approximates the ocular anatomy.Moreover, there is a need for systems and methods that consider avariation in the radius of curvature, which more closely approximatesthe ocular anatomy. Embodiments of the present invention providesolutions for at least some of these needs.

BRIEF SUMMARY OF THE INVENTION

Embodiments of the present invention provide techniques for fine-tuningablation profiles for both conventional non-wavefront andwavefront-driven refractive surgery. These techniques can be implementedin a variety of laser and aberrometer devices, including withoutlimitation the VISX WaveScan WaveFront System and STAR S4 Excimer LaserSystem, the Wavelight Alegretto and Tscherning-based aberrometer; theAlcon Ladarvision lasers and Ladarwave aberrometer; the Bausch and LombZyoptix laser and related aberrometer, and the Zeiss laser and WASCAaberrometer.

Typically the index of refraction of the corneal stroma is not constant.For example, the index of refraction may change from about 1.38 at theanterior surface to about 1.373 at the posterior surface of the cornea.Advantageously, embodiments of the present invention encompasstechniques that consider such a change in the refractive index.Accordingly, it is possible to obtain an improvement in the accuracy ofan ablation profile or treatment shape. In some cases, this involves aconsideration of high order aberrations. Moreover, typically the radiusof curvature of the anterior surface of the cornea is not constant.Advantageously, embodiments of the present invention encompasstechniques that consider a variable corneal radius of curvature.

Embodiments of the present invention encompass accurate techniques thattake into account a change in refractive index of the corneal stroma.Embodiments of the present invention also encompass accurate techniquesthat take into account a customized radius of curvature of the anteriorsurface of the stroma. These techniques can be implemented in, forexample, a VSS refractive treatment.

In one aspect, embodiments of the present invention encompass systemsfor determining a refractive treatment shape for an eye of a patient.Systems may include, for example, an input configured to receive avariable index of refraction for a cornea of the eye, and a processingmodule comprising a tangible medium embodying machine-readable code thatdetermines the refractive treatment shape for the eye based on thevariable index of refraction. In some cases, the refractive treatmentshape can be configured to treat hyperopia or myopia. In some cases, theprocessing module can include a tangible medium embodyingmachine-readable code that determines the refractive treatment shape forthe eye based on a Munnerlyn shape or a wavefront analysis of the eye.Optionally, systems may include an ablation system configured to applythe refractive treatment shape to the patient. The variable index ofrefraction can vary as a function of an ablation depth.

In some aspects, embodiments of the present invention encompass systemsfor determining a refractive treatment shape for an eye of a patient,such that the systems include an input configured to receive aninstantaneous index of refraction for a cornea of the eye, and aprocessing module having a tangible medium embodying machine-readablecode that determines the refractive treatment shape of a remainingablation for the eye based on the instantaneous index of refraction.Systems may also include an ablation system configured to apply therefractive treatment shape to the patient. In some cases, systemsinclude sensor or sensing assembly that detects the instantaneous indexof refraction. The instantaneous index of refraction can vary as afunction of an ablation depth.

In a further aspect, embodiments of the present invention encompasssystems for determining a refractive treatment shape for an eye of apatient, such that a system may include an input configured to receive avariable radius of curvature of an anterior surface of a cornea of theeye, and a processing module with a tangible medium embodyingmachine-readable code that determines the refractive treatment shape forthe eye based on the variable radius of curvature of the anteriorsurface. Systems may also have an ablation system configured to applythe refractive treatment shape to the patient. In some cases, thevariable radius of curvature of the anterior surface of the eye is afunction of a radius of curvature of a posterior surface of the cornea.In some cases, the variable radius of curvature of the anterior surfaceof the eye can vary as a function of an ablation depth.

In another aspect, embodiments of the present invention encompasssystems for determining a refractive treatment shape for an eye of apatient, where a system can have an input configured to receive aninstantaneous radius of curvature of an anterior surface of a cornea ofthe eye, and a processing module with a tangible medium embodyingmachine-readable code that determines the refractive treatment shape ofa remaining ablation for the eye based on the instantaneous radius ofcurvature of the anterior surface of the cornea of the eye. Systems mayalso include an ablation system configured to apply the refractivetreatment shape to the patient. In some cases, systems include a sensoror sensor assembly that detects the instantaneous radius of curvature ofthe anterior surface of the cornea of the eye. The instantaneous radiusof curvature of the anterior surface of the eye can vary as a functionof an ablation depth. The refractive treatment shape for the eye can bebased on a Munnerlyn equation.

In yet another aspect, embodiments of the present invention encompassmethods of determining a refractive treatment shape for an eye of apatient. Methods may include, for example, determining a variable indexof refraction for a cornea of the eye, and determining the refractivetreatment shape for the eye based on the variable index of refraction.In some cases, the step of determining the refractive treatment shapeinvolves determining a refractive treatment shape of a remainingablation for the eye based on the variable index of refraction. In somecases, the variable index of refraction for the cornea varies between ananterior portion of the cornea and a posterior portion of the cornea. Insome cases, the variable index of refraction for the cornea variesacross at least a portion of a corneal stroma. Relatedly, the variableindex of refraction for the cornea can vary as a function of cornealstromal depth. The variable index of refraction for the cornea may varyas a linear function of corneal stromal depth. In some cases, thevariable index of refraction for the cornea varies as a nonlinearfunction of corneal stromal depth. The refractive treatment shape can beconfigured to treat hyperopia. Relatedly, the refractive treatment shapecan be configured to treat myopia. In some cases, the refractivetreatment shape is determined based on a Munnerlyn shape. In some cases,the refractive treatment shape is determined based on a wavefrontanalysis of the eye. The variable index of refraction for the cornea ofthe eye may be determined following application of one or more ablationpulses to the eye. Optionally, the step of determining the variableindex of refraction for a cornea of the eye can include determining aninstantaneous variable index of refraction for the cornea followingapplication of one or more ablation pulses to the eye, and the step ofdetermining the refractive treatment shape can include determining arefractive treatment shape of a remaining ablation for the eye based onthe instantaneous variable index of refraction. Methods may also involveapplying the refractive treatment shape to the eye with an ablationsystem.

In another aspect, embodiments of the present invention encompassmethods of determining a refractive treatment shape for an eye of apatient that include, for example, determining a variable radius ofcurvature of an anterior surface of a cornea of the eye, and determiningthe refractive treatment shape for the eye based on the variable radiusof curvature. In some cases, the step of determining the refractivetreatment shape involves determining a refractive treatment shape of aremaining ablation for the eye based on the variable radius ofcurvature. In some cases, the variable radius of curvature for thecornea of the eye is determined following application of one or moreablation pulses to the eye. Optionally, the step of determining thevariable radius of curvature can include determining an instantaneousvariable radius of curvature for the cornea following application of oneor more ablation pulses to the eye, and the step of determining therefractive treatment shape can include determining a refractivetreatment shape of a remaining ablation for the eye based on theinstantaneous variable radius of curvature. Methods may also includeapplying the refractive treatment shape to the eye with an ablationsystem. In some cases, the variable radius of curvature of the anteriorsurface of the eye varies as a function of cornea thickness. In somecases, the variable radius of curvature of the anterior surface of theeye is a function of a radius of curvature of a posterior surface of thecornea. In some cases, the variable radius of curvature of the anteriorsurface of the eye varies as a function of an ablation depth.Optionally, the refractive treatment shape for the eye can be based on aMunnerlyn equation.

For a fuller understanding of the nature and advantages of the presentinvention, reference should be had to the ensuing detailed descriptiontaken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a laser ablation system according to an embodiment ofthe present invention.

FIG. 2 illustrates a simplified computer system according to anembodiment of the present invention.

FIG. 3 illustrates a wavefront measurement system according to anembodiment of the present invention.

FIG. 3A illustrates another wavefront measurement system according to anembodiment of the present invention.

FIGS. 4A and 4B show aspects of an embodiment of the present invention.

FIG. 5 shows corneal ablation data according to embodiments of thepresent invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention can be readily adapted for use with existing lasersystems, wavefront measurement systems, and other optical measurementdevices. Although the systems, software, and methods of the presentinvention are described primarily in the context of a laser eye surgerysystem, it should be understood the present invention may be adapted foruse in alternative eye treatment procedures, systems, or modalities,such as spectacle lenses, intraocular lenses, accommodating IOLs,contact lenses, corneal ring implants, collagenous corneal tissuethermal remodeling, corneal inlays, corneal onlays, other cornealimplants or grafts, and the like. Relatedly, systems, software, andmethods according to embodiments of the present invention are wellsuited for customizing any of these treatment modalities to a specificpatient. Thus, for example, embodiments encompass custom intraocularlenses, custom contact lenses, custom corneal implants, and the like,which can be configured to treat or ameliorate any of a variety ofvision conditions in a particular patient based on their unique ocularcharacteristics or anatomy.

Turning now to the drawings, FIG. 1 illustrates a laser eye surgerysystem 10 of the present invention, including a laser 12 that produces alaser beam 14. Laser 12 is optically coupled to laser delivery optics16, which directs laser beam 14 to an eye E of patient P. A deliveryoptics support structure (not shown here for clarity) extends from aframe 18 supporting laser 12. A microscope 20 is mounted on the deliveryoptics support structure, the microscope often being used to image acornea of eye E.

Laser 12 generally comprises an excimer laser, ideally comprising anargon-fluorine laser producing pulses of laser light having a wavelengthof approximately 193 nm. Laser 12 will preferably be designed to providea feedback stabilized fluence at the patient's eye, delivered viadelivery optics 16. The present invention may also be useful withalternative sources of ultraviolet or infrared radiation, particularlythose adapted to controllably ablate the corneal tissue without causingsignificant damage to adjacent and/or underlying tissues of the eye.Such sources include, but are not limited to, solid state lasers andother devices which can generate energy in the ultraviolet wavelengthbetween about 185 and 205 nm and/or those which utilizefrequency-multiplying techniques. Hence, although an excimer laser isthe illustrative source of an ablating beam, other lasers may be used inthe present invention.

Laser system 10 will generally include a computer or programmableprocessor 22. Processor 22 may comprise (or interface with) aconventional PC system including the standard user interface devicessuch as a keyboard, a display monitor, and the like. Processor 22 willtypically include an input device such as a magnetic or optical diskdrive, an internet connection, or the like. Such input devices willoften be used to download a computer executable code from a tangiblestorage media 29 embodying any of the methods of the present invention.Tangible storage media 29 may take the form of a floppy disk, an opticaldisk, a data tape, a volatile or non-volatile memory, RAM, or the like,and the processor 22 will include the memory boards and other standardcomponents of modern computer systems for storing and executing thiscode. Tangible storage media 29 may optionally embody wavefront sensordata, wavefront gradients, a wavefront elevation map, a treatment map, acorneal elevation map, and/or an ablation table. While tangible storagemedia 29 will often be used directly in cooperation with a input deviceof processor 22, the storage media may also be remotely operativelycoupled with processor by means of network connections such as theinternet, and by wireless methods such as infrared, Bluetooth, or thelike.

Laser 12 and delivery optics 16 will generally direct laser beam 14 tothe eye of patient P under the direction of a computer 22. Computer 22will often selectively adjust laser beam 14 to expose portions of thecornea to the pulses of laser energy so as to effect a predeterminedsculpting of the cornea and alter the refractive characteristics of theeye. In many embodiments, both laser beam 14 and the laser deliveryoptical system 16 will be under computer control of processor 22 toeffect the desired laser sculpting process, with the processor effecting(and optionally modifying) the pattern of laser pulses. The pattern ofpulses may by summarized in machine readable data of tangible storagemedia 29 in the form of a treatment table, and the treatment table maybe adjusted according to feedback input into processor 22 from anautomated image analysis system in response to feedback data providedfrom an ablation monitoring system feedback system. Optionally, thefeedback may be manually entered into the processor by a systemoperator. Such feedback might be provided by integrating the wavefrontmeasurement system described below with the laser treatment system 10,and processor 22 may continue and/or terminate a sculpting treatment inresponse to the feedback, and may optionally also modify the plannedsculpting based at least in part on the feedback. Measurement systemsare further described in U.S. Pat. No. 6,315,413, the full disclosure ofwhich is incorporated herein by reference.

Laser beam 14 may be adjusted to produce the desired sculpting using avariety of alternative mechanisms. The laser beam 14 may be selectivelylimited using one or more variable apertures. An exemplary variableaperture system having a variable iris and a variable width slit isdescribed in U.S. Pat. No. 5,713,892, the full disclosure of which isincorporated herein by reference. The laser beam may also be tailored byvarying the size and offset of the laser spot from an axis of the eye,as described in U.S. Pat. Nos. 5,683,379, 6,203,539, and 6,331,177, thefull disclosures of which are incorporated herein by reference.

Still further alternatives are possible, including scanning of the laserbeam over the surface of the eye and controlling the number of pulsesand/or dwell time at each location, as described, for example, by U.S.Pat. No. 4,665,913, the full disclosure of which is incorporated hereinby reference; using masks in the optical path of laser beam 14 whichablate to vary the profile of the beam incident on the cornea, asdescribed in U.S. Pat. No. 5,807,379, the full disclosure of which isincorporated herein by reference; hybrid profile-scanning systems inwhich a variable size beam (typically controlled by a variable widthslit and/or variable diameter iris diaphragm) is scanned across thecornea; or the like. The computer programs and control methodology forthese laser pattern tailoring techniques are well described in thepatent literature.

Additional components and subsystems may be included with laser system10, as should be understood by those of skill in the art. For example,spatial and/or temporal integrators may be included to control thedistribution of energy within the laser beam, as described in U.S. Pat.No. 5,646,791, the full disclosure of which is incorporated herein byreference. Ablation effluent evacuators/filters, aspirators, and otherancillary components of the laser surgery system are known in the art.Further details of suitable systems for performing a laser ablationprocedure can be found in commonly assigned U.S. Pat. Nos. 4,665,913,4,669,466, 4,732,148, 4,770,172, 4,773,414, 5,207,668, 5,108,388,5,219,343, 5,646,791 and 5,163,934, the complete disclosures of whichare incorporated herein by reference. Suitable systems also includecommercially available refractive laser systems such as thosemanufactured and/or sold by Alcon, Bausch & Lomb, Nidek, WaveLight,LaserSight, Schwind, Zeiss-Meditec, and the like. Basis data can befurther characterized for particular lasers or operating conditions, bytaking into account localized environmental variables such astemperature, humidity, airflow, and aspiration.

FIG. 2 is a simplified block diagram of an exemplary computer system 22that may be used by the laser surgical system 10 of the presentinvention. Computer system 22 typically includes at least one processor52 which may communicate with a number of peripheral devices via a bussubsystem 54. These peripheral devices may include a storage subsystem56, comprising a memory subsystem 58 and a file storage subsystem 60,user interface input devices 62, user interface output devices 64, and anetwork interface subsystem 66. Network interface subsystem 66 providesan interface to outside networks 68 and/or other devices, such as thewavefront measurement system 30.

User interface input devices 62 may include a keyboard, pointing devicessuch as a mouse, trackball, touch pad, or graphics tablet, a scanner,foot pedals, a joystick, a touchscreen incorporated into the display,audio input devices such as voice recognition systems, microphones, andother types of input devices. User input devices 62 will often be usedto download a computer executable code from a tangible storage media 29embodying any of the methods of the present invention. In general, useof the term “input device” is intended to include a variety ofconventional and proprietary devices and ways to input information intocomputer system 22.

User interface output devices 64 may include a display subsystem, aprinter, a fax machine, or non-visual displays such as audio outputdevices. The display subsystem may be a cathode ray tube (CRT), aflat-panel device such as a liquid crystal display (LCD), a projectiondevice, or the like. The display subsystem may also provide a non-visualdisplay such as via audio output devices. In general, use of the term“output device” is intended to include a variety of conventional andproprietary devices and ways to output information from computer system22 to a user.

Storage subsystem 56 can store the basic programming and data constructsthat provide the functionality of the various embodiments of the presentinvention. For example, a database and modules implementing thefunctionality of the methods of the present invention, as describedherein, may be stored in storage subsystem 56. These software modulesare generally executed by processor 52. In a distributed environment,the software modules may be stored on a plurality of computer systemsand executed by processors of the plurality of computer systems. Storagesubsystem 56 typically comprises memory subsystem 58 and file storagesubsystem 60.

Memory subsystem 58 typically includes a number of memories including amain random access memory (RAM) 70 for storage of instructions and dataduring program execution and a read only memory (ROM) 72 in which fixedinstructions are stored. File storage subsystem 60 provides persistent(non-volatile) storage for program and data files, and may includetangible storage media 29 (FIG. 1) which may optionally embody wavefrontsensor data, wavefront gradients, a wavefront elevation map, a treatmentmap, and/or an ablation table. File storage subsystem 60 may include ahard disk drive, a floppy disk drive along with associated removablemedia, a Compact Digital Read Only Memory (CD-ROM) drive, an opticaldrive, DVD, CD-R, CD-RW, solid-state removable memory, and/or otherremovable media cartridges or disks. One or more of the drives may belocated at remote locations on other connected computers at other sitescoupled to computer system 22. The modules implementing thefunctionality of the present invention may be stored by file storagesubsystem 60.

Bus subsystem 54 provides a mechanism for letting the various componentsand subsystems of computer system 22 communicate with each other asintended. The various subsystems and components of computer system 22need not be at the same physical location but may be distributed atvarious locations within a distributed network. Although bus subsystem54 is shown schematically as a single bus, alternate embodiments of thebus subsystem may utilize multiple busses.

Computer system 22 itself can be of varying types including a personalcomputer, a portable computer, a workstation, a computer terminal, anetwork computer, a control system in a wavefront measurement system orlaser surgical system, a mainframe, or any other data processing system.Due to the ever-changing nature of computers and networks, thedescription of computer system 22 depicted in FIG. 2 is intended only asa specific example for purposes of illustrating one embodiment of thepresent invention. Many other configurations of computer system 22 arepossible having more or less components than the computer systemdepicted in FIG. 2.

Referring now to FIG. 3, one embodiment of a wavefront measurementsystem 30 is schematically illustrated in simplified form. In verygeneral terms, wavefront measurement system 30 is configured to senselocal slopes of a gradient map exiting the patient's eye. Devices basedon the Hartmann-Shack principle generally include a lenslet array tosample the gradient map uniformly over an aperture, which is typicallythe exit pupil of the eye. Thereafter, the local slopes of the gradientmap are analyzed so as to reconstruct the wavefront surface or map.

More specifically, one wavefront measurement system 30 includes an imagesource 32, such as a laser, which projects a source image throughoptical tissues 34 of eye E so as to form an image 44 upon a surface ofretina R. The image from retina R is transmitted by the optical systemof the eye (e.g., optical tissues 34) and imaged onto a wavefront sensor36 by system optics 37. The wavefront sensor 36 communicates signals toa computer system 22′ for measurement of the optical errors in theoptical tissues 34 and/or determination of an optical tissue ablationtreatment program. Computer 22′ may include the same or similar hardwareas the computer system 22 illustrated in FIGS. 1 and 2. Computer system22′ may be in communication with computer system 22 that directs thelaser surgery system 10, or some or all of the components of computersystem 22, 22′ of the wavefront measurement system 30 and laser surgerysystem 10 may be combined or separate. If desired, data from wavefrontsensor 36 may be transmitted to a laser computer system 22 via tangiblemedia 29, via an I/O port, via an networking connection 66 such as anintranet or the Internet, or the like.

Wavefront sensor 36 generally comprises a lenslet array 38 and an imagesensor 40. As the image from retina R is transmitted through opticaltissues 34 and imaged onto a surface of image sensor 40 and an image ofthe eye pupil P is similarly imaged onto a surface of lenslet array 38,the lenslet array separates the transmitted image into an array ofbeamlets 42, and (in combination with other optical components of thesystem) images the separated beamlets on the surface of sensor 40.Sensor 40 typically comprises a charged couple device or “CCD,” andsenses the characteristics of these individual beamlets, which can beused to determine the characteristics of an associated region of opticaltissues 34. In particular, where image 44 comprises a point or smallspot of light, a location of the transmitted spot as imaged by a beamletcan directly indicate a local gradient of the associated region ofoptical tissue.

Eye E generally defines an anterior orientation ANT and a posteriororientation POS. Image source 32 generally projects an image in aposterior orientation through optical tissues 34 onto retina R asindicated in FIG. 3. Optical tissues 34 again transmit image 44 from theretina anteriorly toward wavefront sensor 36. Image 44 actually formedon retina R may be distorted by any imperfections in the eye's opticalsystem when the image source is originally transmitted by opticaltissues 34. Optionally, image source projection optics 46 may beconfigured or adapted to decrease any distortion of image 44.

In some embodiments, image source optics 46 may decrease lower orderoptical errors by compensating for spherical and/or cylindrical errorsof optical tissues 34. Higher order optical errors of the opticaltissues may also be compensated through the use of an adaptive opticelement, such as a deformable mirror (described below). Use of an imagesource 32 selected to define a point or small spot at image 44 uponretina R may facilitate the analysis of the data provided by wavefrontsensor 36. Distortion of image 44 may be limited by transmitting asource image through a central region 48 of optical tissues 34 which issmaller than a pupil 50, as the central portion of the pupil may be lessprone to optical errors than the peripheral portion. Regardless of theparticular image source structure, it will be generally be beneficial tohave a well-defined and accurately formed image 44 on retina R.

In one embodiment, the wavefront data may be stored in a computerreadable medium 29 or a memory of the wavefront sensor system 30 in twoseparate arrays containing the x and y wavefront gradient valuesobtained from image spot analysis of the Hartmann-Shack sensor images,plus the x and y pupil center offsets from the nominal center of theHartmann-Shack lenslet array, as measured by the pupil camera 51 (FIG.3) image. Such information contains all the available information on thewavefront error of the eye and is sufficient to reconstruct thewavefront or any portion of it. In such embodiments, there is no need toreprocess the Hartmann-Shack image more than once, and the data spacerequired to store the gradient array is not large. For example, toaccommodate an image of a pupil with an 8 mm diameter, an array of a20×20 size (i.e., 400 elements) is often sufficient. As can beappreciated, in other embodiments, the wavefront data may be stored in amemory of the wavefront sensor system in a single array or multiplearrays.

While the methods of the present invention will generally be describedwith reference to sensing of an image 44, a series of wavefront sensordata readings may be taken. For example, a time series of wavefront datareadings may help to provide a more accurate overall determination ofthe ocular tissue aberrations. As the ocular tissues can vary in shapeover a brief period of time, a plurality of temporally separatedwavefront sensor measurements can avoid relying on a single snapshot ofthe optical characteristics as the basis for a refractive correctingprocedure. Still further alternatives are also available, includingtaking wavefront sensor data of the eye with the eye in differingconfigurations, positions, and/or orientations. For example, a patientwill often help maintain alignment of the eye with wavefront measurementsystem 30 by focusing on a fixation target, as described in U.S. Pat.No. 6,004,313, the full disclosure of which is incorporated herein byreference. By varying a position of the fixation target as described inthat reference, optical characteristics of the eye may be determinedwhile the eye accommodates or adapts to image a field of view at avarying distance and/or angles.

The location of the optical axis of the eye may be verified by referenceto the data provided from a pupil camera 52. In the exemplaryembodiment, a pupil camera 52 images pupil 50 so as to determine aposition of the pupil for registration of the wavefront sensor datarelative to the optical tissues.

An alternative embodiment of a wavefront measurement system isillustrated in FIG. 3A. The major components of the system of FIG. 3Aare similar to those of FIG. 3. Additionally, FIG. 3A includes anadaptive optical element 53 in the form of a deformable mirror. Thesource image is reflected from deformable mirror 98 during transmissionto retina R, and the deformable mirror is also along the optical pathused to form the transmitted image between retina R and imaging sensor40. Deformable mirror 98 can be controllably deformed by computer system22 to limit distortion of the image formed on the retina or ofsubsequent images formed of the images formed on the retina, and mayenhance the accuracy of the resultant wavefront data. The structure anduse of the system of FIG. 3A are more fully described in U.S. Pat. No.6,095,651, the full disclosure of which is incorporated herein byreference.

The components of an embodiment of a wavefront measurement system formeasuring the eye and ablations may comprise elements of a WaveScan®system, available from VISX, INCORPORATED of Santa Clara, Calif. Oneembodiment includes a WaveScan system with a deformable mirror asdescribed above. An alternate embodiment of a wavefront measuring systemis described in U.S. Pat. No. 6,271,915, the full disclosure of which isincorporated herein by reference. It is appreciated that any wavefrontaberrometer could be employed for use with the present invention.Relatedly, embodiments of the present invention encompass theimplementation of any of a variety of optical instruments provided byWaveFront Sciences, Inc., including the COAS wavefront aberrometer, theClearWave contact lens aberrometer, the CrystalWave IOL aberrometer, andthe like.

Embodiments of the present invention encompass techniques that considerthe index of refraction for corneal stroma as a function of depth orradial distance, and the radius of curvature variation as a laserablates deeper and deeper tissue.

Using a Munnerlyn equation, it can be calculated that as the tissue isbeing ablated, each diopter of ablation has a smaller value ofrefractive index and larger value of the radius of curvature for myopiaand a smaller value of the radius of curvature of the cornea forhyperopia, as the ablation goes deeper and deeper. In consequence, for a−6 D ablation, a 2% overcorrection can be estimated. For a +6 Dablation, a 2% undercorrection can be evaluated.

Excimer laser refractive surgery has been proven as a favorable visioncorrection means. It is often desirable to achieve a correction ortreatment of the low order spherocylindrical error. Moreover, it is alsodesirable to achieve a favorable outcome of the refractive correction ofocular aberrations. Any small deviation may affect the final outcome ofthe surgery.

Embodiments of the present invention encompass techniques that canaddress factors which may affect a precise correction of low orderaberrations or otherwise induce some high order aberrations, preventinga complete or desired correction of ocular aberrations. A methodologyused for evaluating the possible error due to an imperfect system isdescribed in G.-m. Dai et al. “System performance evaluation ofrefractive surgical lasers: a mathematical approach,” Appl. Opt. 45,2124-2134 (2006), which is incorporated herein by reference for allpurposes.

Variable Index of Refraction of the Cornea

The refractive index may be dependent on the frequency of light. In someembodiments, only the indices at visible light are considered. In someembodiments, indices at other frequencies are considered. The refractiveindex of the corneal stroma may be assumed to be a constant by taking anaverage of the values of the anterior and posterior surfaces of thestroma. This is an approximation. The refractive index of the stroma mayvary vertically and horizontally. Aspects of this variation arediscussed in M. Dubbelman et al. “The shape of the aging human lens:curvature, equivalent refractive index and the lens paradox,” Vis. Res.41, 1867-1877 (2001), which is incorporated herein by reference for allpurposes. The refractive index can be higher toward the periphery of thestroma, and lower toward the center of the stroma. Relatedly, therefractive index can be higher toward the anterior stroma, and lowertoward the posterior stroma.

It is possible to denote n(h) as the refractive index of the stroma atthe ablation depth h, and the refractive index of the stroma as

n(h)=n _(o) +δh,  (1)

where the refractive index of the outermost layer of the stroma n₀=1.38and the mean gradient index of the stromaδ=(1.373-1.38)/5.5×10^(−4=−12.73) m⁻¹. In Eq. (1), a nominal value of550 μm for the thickness of the cornea can be assumed. For example, whenthe stroma is ablated for 50 μm, the refractive index is reduced from1.38 to 1.38-12.73×50×10⁻⁶=1.379. When the entire stroma of 550 μm isablated, the refractive index can drop to 1.373.

In some embodiments, instead of using a nominal value of 1.376 for therefractive index of the stroma, it is possible to use Eq. (1) torepresent the refractive index of the stroma as a function of theablation depth h where n₀ is the refractive index of the stroma at thesurface, and is 1.379. For surface ablations, such as LASEK and PRK, Eq.(1) can be used such that n₀=1.39 is the refractive index of theanterior surface of the stroma. When it is used for LASIK, n₀ may dependupon the thickness of the LASIK flap. For example, for normal flapthickness of 160 microns, n₀ can be 1.3770. For thin flaps of 110microns that can be created with IntraLase femtosecond lasers, n₀ can be1.3776.

Table 1 shows the ablation depth for every diopter of myopia andhyperopia for different levels of refractions with a 6 mm optical zone.Optionally, these values can be calculated using the Munnerlyn equation.Relatedly, Table 1 can provide the basis for an example for a deviationfrom a Munnerlyn equation on a per diopter situation. For a myopicablation, the per diopter ablation depth becomes less deep as theablation progresses. In comparison, for a hyperopic ablation, the perdiopter ablation depth becomes deeper as the ablation continues. Hence,there can be a nonlinear relationship between the ablation depth andpower, for example. According to some embodiments, the variable index ofrefraction for the cornea varies as a function of corneal stromal depth.In some cases, the function in Eq. (1) is linear. However, theper-diopter depth of ablation as a function of the ablation depth can benon-linear. Table 1 shows an ablation depth per diopter as a function ofthe sphere of myopia and hyperopia. An optical zone O=6 mm and thepre-surgery corneal radius of curvature R₁=7.8 mm are assumed. In somecases, techniques may involve ablation depth per partial diopter as afunction of the sphere or myopia or hyperopia. Partial diopters caninclude half diopters, quarter diopters, and the like. In some cases,partial diopters can be considered as infinitesimally small orapproaching zero, for example.

TABLE 1 Myopia Hyperopia Sphere R₁ Depth R₁ Depth (D) n (mm) (μm) (mm)(μm) 1 1.3799 7.80 13.310 7.80 13.381 2 1.3797 7.96 13.248 7.64 13.459 31.3796 8.13 13.188 7.49 13.541 4 1.3794 8.31 13.130 7.35 13.625 5 1.37928.50 13.074 7.21 13.711 6 1.3791 8.69 13.019 7.07 13.800 7 1.3789 8.9012.967 6.94 13.893 8 1.3787 9.11 12.917 6.82 13.988 9 1.3786 9.34 12.8686.70 14.086 10 1.3784 9.57 12.821 6.58 14.187

Based on Table 1, it is apparent that for a myopia treatment, theablation depth can change from about 13.31 microns for the first diopterto about 12.82 microns for the tenth diopter. Similarly, for a hyperopiatreatment, the ablation depth can change from about 13.38 microns forthe first diopter to about 14.19 microns for the tenth diopter.

As an exemplary illustration, for a −6 D myopic eye it is possible tocalculate the deviation of true depth using variable refractive index ascompared to using the mean refractive index for O=6 mm optical zone.Consider for example that a depth per diopter myopia is 13.43 μm so thetotal depth for a −6 D eye is 13.43×6=80.58 μm. To calculate the depthwith the variable refractive index, adding the first six values in Table1 for myopia, it is possible to obtain 78.97 μm. Therefore, the fixedrefractive index model over-ablates a −6 D myopic eye by80.58-78.97=1.611 μm. This is a 2% overcorrection.

As an ablation continues, the index of refraction of the resultinganterior stromal layer can change. Hence, a variable index of refractioncan vary as a function of ablation depth. In some cases, embodiments ofthe present invention encompass techniques that incorporate aprecalculated variable index of refraction. In some cases, embodimentsencompass techniques that incorporate an ongoing or instantaneousrefinement of the variable index of refraction calculation. In otherwords, a variable index determination can be used to drive a treatmentfrom the start, and can also be used to form the basis for providingongoing refinement of a treatment according to a closed-loop process.For example, a method of determining a refractive treatment shape caninclude determining an instantaneous index of refraction at one or moretimes during an ablation treatment, and determining or refining therefractive treatment shape based on the instantaneous index ofrefraction. Optionally, a method of determining a refractive treatmentshape can include determining a variable index of refraction, anddetermining the refractive treatment shape of the remaining ablation forthe eye based on the variable index of refraction. As the ablationprogresses, the index of refraction can change as additional material isablated.

In an open loop approach, a variable index of refraction can be based ona precalculated or predicted value. For example, a look-up table can beconstructed such that the depth of the ablation profile can be foundbased on the refraction of the eye. Optionally, an infinitesimally thinprofile can be constructed based upon the Munnerlyn equation or thewavefront-driven parabolic shape and an integration can be performedover the refraction of the eye when determining a final ablationprofile. In a closed loop approach, an index of refraction can bemonitored in real time during an ablation procedure, and ablationtreatment parameters can be adjusted or refined based on theinstantaneous refractive index or refractive index change. In somecases, the index of refraction can be measured following the applicationof one or more ablation pulses applied to the eye. The residual ablationprofile can be determined based on the ablated profile and theinstantaneous refractive index such that the final ablated profile whenthe ablation is complete optimally matches the planned ablation profile.

The depth of an ablation and the shape of tissue removed can vary basedon the variable index of refraction. Variable index of refractions mayvary between different patients. Embodiments disclosed herein providetissue refractive index measurement and ablation systems suitable forintegration with known laser eye surgery systems. Embodiments alsoencompass techniques that provide diagnostic information before, and/orfeedback information during, a corneal resculpting procedure.Information regarding the index of refraction of the cornea orcomponents of the cornea can be used to establish or modify aresculpting laser energy pattern for a corneal tissue surface.

Embodiments encompass systems and methods for measuring or detecting theindex of refraction of a corneal or stromal tissue using, for example, aScheimflug imaging technique. M. Dubbleman et al. discuss a method fordetermining the refractive index of the crystalline lens in “The shapeof the aging human lens: curvature, equivalent refractive index and thelens paradox,” Vis. Res. 41, 1867-1877 (2001), the entirety of which isincorporated herein by reference for all purposes. Systems may include aprocessor coupled with, in communication with, or otherwise configuredto receive information from the sensor, whereby the processor cangenerate a refractive index signal indicating the refractive index ofthe tissue. Relatedly, embodiments encompass systems and methods forresculpting a corneal tissue of an eye. Systems may include an apparatusthat directs a pattern of light energy from a laser under the directionof a processor to effect a desired change in an optical characteristicof the eye, and an adjustment module of a system processor can vary thepattern in response to the index of refraction information from asensor.

In some cases, embodiments encompass compensation techniques for use ina procedure for resculpting a corneal tissue of an eye. A resculptingprocedure can selectively direct a pattern of laser energy toward theeye to effect a predetermined change in an optical characteristic of theeye. A compensation method may include sensing or detecting a refractiveindex of the corneal or stromal tissue of the eye, and adjusting thepattern of laser energy in response to the sensed refractive index. Anablation energy delivery system can be coupled to a processor, thedelivery system can direct an ablative energy toward the tissue, and theprocessor can vary the ablative energy in response to a refractive indexsignal. The tissue will typically include a corneal tissue of an eye,and the delivery system may include an optical delivery systemtransmitting photoablative laser energy toward the corneal tissue so asto selectively alter an optical characteristic of the eye. The processormay vary a quantity of change in the optical characteristic of the eyein response to the refractive index signal. For example, the processormay vary a diopter value of the resculpting procedure in response to theindex of refraction. Alternatively, the processor may vary the shape ofthe ablation by altering the ablative energy pattern so as to compensatefor local differences in refractive index across the target region ofthe corneal tissue. In some embodiments, an output device coupled to theprocessor may show a display in response to the index of refractionsignal.

Systems and methods for sculpting of a conical tissue of an eye toeffect a desired change in an optical property are also provided herein.Such techniques can include sensing or detecting an index of refractionof a stromal tissue of the eye, and determining a desired change inshape of the eye in response to the index of refraction, and in responseto the desired change in optical property. A pattern of laser energy canbe planned for directing toward the conical tissue, so as to effect thedetermined change in shape. A desired change in optical quality can bedetermined while the tissue has a initial index of refraction, or asubsequent index of refraction following or during an ablation orresculpting step. The change in optical quality may be determined usingany of a variety of standard vision diagnostic systems. Wavefront sensorsystems now being developed may also be beneficial for determining adesired change in an optical property, and still further alternativetopography and/or tomography systems may also be used. Regardless,rather than simply determining the desired change in shape of the eyefrom such measurements alone, the desired sculpting or ablation shapecan also be based in part on the index of refraction of the eye.

An exemplary method for performing a refractive index compensatedphotorefractive ablation may be initiated using a predetermined ablationpattern assuming a standard ablation rate. A sensor can be used todetermine or evaluate the refractive index of stromal tissue of the eye.The standard ablation rate can be adjusted based on the refractiveindex, and the adjusted ablation rate can be part of a treatment patternof ablation energy directed toward the tissue so as to effect thedesired change in optical characteristics of eye. The treatment pattern,can include parameters such as the size, location, and/or number oflaser pulses directed toward some or all of the treatment region of theeye. One or more of these parameters can be set or adjusted based on therefractive index. In some cases, an algorithm used to calculate a shotpattern so as to effect a desired change in corneal shape mayincorporate adjusted ablation rates appropriate for a varying index ofrefraction.

As noted above, a refractive index can vary vertically based on stromaldepth. A refractive index can also vary horizontally based on a functionof radial distance from a central portion of the stroma. Radialdependency of the refractive index can characterize a stroma that has alower index of refraction in a central portion of the stroma. In someeases, radial dependency can be characterized with the followingformula: n(r)=n₀+λr, where r represents the radial distance from acentral portion of the stroma, and λ represents the rate of change ofthe refractive index radially. Thus, it is possible to denote n(r) asthe refractive index of the stroma at the radial distance r, where therefractive index of a central portion of the stroma is n₀, which candepend on the ablation depth. On the anterior surface of the cornea, itis about 1.38. On the anterior surface of the stroma, it is about 1.379.On the posterior surface of the stroma, it is about 1.373.

In some embodiments, techniques involve determining the variability of arefractive index of a patient, and determining a refractive treatmentshape based on that variability. These approaches can be used todetermine a treatment shape based on modification of a Munnerlyn shape.Optionally, these approaches can be used to determine a treatment shapebased on a wavefront analysis.

Variable Corneal Radius of Curvature

In one approximation, the corneal radius of curvature can be consideredas a constant. Some equations, such as the Munnerlyn equation, canincorporate this assumption. A relationship between the radius ofcurvature of the anterior surface of the cornea R₁ and the keratometryor keratometric power F can be expressed by

$\begin{matrix}{{R_{1} = \frac{( {n - 1} )\lbrack {R_{2} + {( {n - n_{2}} )d}} \rbrack}{{R_{2}F} + {( {n - n_{2}} )( {1 + {Fd}} )}}},} & (2)\end{matrix}$

where n and n₂ are the refractive indices of the anterior and posteriorsurfaces [of the cornea?], respectively, d is the cornea thickness orpachymetry, and R₂ is the radius of curvature of the posterior surfaceof the cornea. Because the values of d and R₂ typically vary from eye toeye, the calculated R₁ can also vary.

FIG. 4A illustrates a radius of curvature of the anterior surface of thecornea as a function of pachymetry or cornea thickness (R₂=6.4 mm). Thisfigure shows the variability for the calculation of the radius ofcurvature of the anterior surface of the cornea as a function of thepachymetry, according to some embodiments. FIG. 4B illustrates a radiusof curvature of the anterior surface of the cornea as a function of theradius of curvature of the posterior surface of the cornea (d=550 μm).Refractive indices n=1.3765 and n₂=1.336 are assumed. These figures showthe variability for the calculation of the radius of curvature of theanterior surface of the cornea as a function of the radius of curvatureof the posterior surface of the cornea, according to some embodiments.It is quite clear that the variability of R₂ gives the variability ofR₁.

As an exemplary illustration, it is possible to calculate the deviationof the tissue ablation depth for a +1 D hyperopic eye using a 6 mmoptical zone, when the radius of curvatures of the anterior andposterior surfaces of the cornea are taken as 6.4 mm and 7.5 mm,respectively. The keratometry and pachymetry are assumed to be 45 D and550 μm, respectively.

From Eq. (2), for R₂=6.4 mm, F=45 D, and d=550 μm, it is possible toobtainR₁=(1.3765−1)×[0.0064+(1.3765−1.336)×0.00055]/[0.0064×45+(1.3765−1.336)×(1+45×0.00055)]m=7.34 mm. Similarly, for R₂=7.5 mm, it is possible to obtain R₁=7.47mm. Substituting the two values of R₁ into the Munnerlyn equation Eq.(4), it is possible to obtain the depths as 13.73 μm and 13.66 μm,respectively. This example shows that a variability of about 20% on thevalue of R₂ can lead to about 0.5% mis-correction on the ablationprofile.

Munnerlyn equations for myopia [Eq. (3)], and for hyperopia [Eq. (4)]can be expressed as follows.

$\begin{matrix}{{l(r)} = {\sqrt{R_{1}^{2} - r^{2}} - \sqrt{\lbrack \frac{( {n - 1} )R_{1}}{n - 1 + {SR}_{1}} \rbrack^{2} - r^{2}} + \sqrt{\lbrack \frac{( {n - 1} )R_{1}}{n - 1 + {SR}_{1}} \rbrack^{2} - ( {O/2} )^{2}} - \sqrt{R_{1}^{2} - ( {O/2} )^{2}}}} & (3) \\{\mspace{79mu} {{l(r)} = {\sqrt{R_{1}^{2} - r^{2}} - R_{1} + \frac{( {n - 1} )R_{1}}{n - 1 + {SR}_{1}} - \sqrt{\lbrack \frac{( {n - 1} )R_{1}}{n - 1 + {SR}_{1}} \rbrack - r^{2}}}}} & (4)\end{matrix}$

Accordingly, embodiments of the present invention encompass techniqueswhere an anterior radius of curvature can be incorporated into aMunnerlyn equation. Anterior optical surfaces may vary from person toperson, and ablations may effect an anterior surface feature.

According to some embodiments, as the ablation progresses, the conicalradius of curvature can change. For example, as the ablation continuesin a myopia treatment, the radius of curvature of the anterior corneacan become larger and larger. Relatedly, as the ablation continues in ahyperopia treatment, the radius of curvature of the anterior cornea canbecome smaller and smaller. Hence, a variable radius of curvature of theanterior surface of the eye can vary as a function of the ablationdepth. Accordingly, embodiments of the present invention encompasstechniques that incorporate ongoing or instantaneous refinement of thevariable radius of curvature of the anterior surface calculation. Inother words, a variable radius of curvature determination can be used todrive a treatment from the start, and can also be used to form the basisfor providing ongoing refinement of a treatment according to aclosed-loop process. For example, a method of determining a refractivetreatment shape can include determining an instantaneous radius ofcurvature of the anterior surface at one or more times during anablation treatment, and determining or refining the refractive treatmentshape based on the instantaneous radius of curvature of the anteriorsurface. Optionally, a method of determining a refractive treatmentshape can include determining a variable radius of curvature of theanterior surface, and determining the refractive treatment shape of theremaining ablation for the eye based on the variable radius of curvatureof the anterior surface. As the ablation progresses, the radius ofcurvature of the anterior surface can change or vary as additionalmaterial is ablated. Thus, embodiments of the present inventionencompass techniques for determining a refractive treatment shape thatinclude determining the instantaneous keratometry as the ablationcontinues, and determining the refractive treatment shape for theremaining ablation based on the instantaneous keratometry.

As an ablation continues, the anterior corneal radius of curvature canchange. Hence, a variable index of refraction can vary as a function ofthe anterior corneal radius of curvature. In some cases, embodiments ofthe present invention encompass techniques that incorporate aprecalculated variable anterior corneal radius of curvature. In somecases, embodiments encompass techniques that incorporate an ongoing orinstantaneous refinement of the variable anterior corneal radius ofcurvature calculation. In other words, a variable anterior conicalradius of curvature determination can be used to drive a treatment fromthe start, and can also be used to form the basis for providing ongoingrefinement of a treatment according to a closed-loop process. Forexample, a method of determining a refractive treatment shape caninclude determining an instantaneous anterior conical radius ofcurvature at one or more times during an ablation treatment, anddetermining or refining the refractive treatment shape based on theinstantaneous anterior conical radius of curvature. Optionally, a methodof determining a refractive treatment shape can include determining avariable anterior corneal radius of curvature, and determining therefractive treatment shape of the remaining ablation for the eye basedon the variable anterior conical radius of curvature. As the ablationprogresses, the anterior conical radius of curvature can change asadditional material is ablated.

In an open loop approach, a variable anterior conical radius ofcurvature can be based on a precalculated or predicted value. Forexample, this value can be based on the keratometry measurements of theeye. Optionally, an infinitesimally thin profile can be constructedbased upon the Munnerlyn equation or the wavefront-driven parabolicshape and an integration can be performed over the refraction of the eyeto determine a final ablation profile. In a closed loop approach, ananterior corneal radius of curvature can be monitored in real timeduring an ablation procedure, and ablation treatment parameters can beadjusted or refined based on the instantaneous anterior conical radiusof curvature or anterior conical radius of curvature change. In somecases, the anterior corneal radius of curvature can be measuredfollowing the application of one or more ablation pulses applied to theeye.

The depth of an ablation and the shape of tissue removed can vary basedon the variable anterior corneal radius of curvature. Variable anteriorcorneal radius of curvatures may vary between different patients.Embodiments disclosed herein provide tissue radius of curvaturemeasurement and ablation systems suitable for integration with knownlaser eye surgery systems. Embodiments also encompass techniques thatprovide diagnostic information before, and/or feedback informationduring, a conical resculpting procedure. Information regarding theanterior conical radius of curvature can be used to establish or modifya resculpting laser energy pattern for a conical tissue surface.

Embodiments encompass systems and methods for measuring or detecting theanterior conical radius of curvature. Systems may include a processorcoupled with, in communication with, or otherwise configured to receiveinformation from the sensor, whereby the processor can generate ananterior corneal radius of curvature signal indicating the anteriorconical radius of curvature. Relatedly, embodiments encompass systemsand methods for resculpting a conical tissue of an eye. Systems mayinclude an apparatus that directs a pattern of light energy from a laserunder the direction of a processor to effect a desired change in anoptical characteristic of the eye, and an adjustment module of a systemprocessor can vary the pattern in response to the anterior cornealradius of curvature information from a sensor.

In some cases, embodiments encompass compensation techniques for use ina procedure for resculpting a conical tissue of an eye. A resculptingprocedure can selectively direct a pattern of laser energy toward theeye to effect a predetermined change in an optical characteristic of theeye. A compensation method may include sensing or detecting an anteriorconical radius of curvature, and adjusting the pattern of laser energyin response to the sensed anterior corneal radius of curvature. Anablation energy delivery system can be coupled to a processor, thedelivery system can direct an ablative energy toward the tissue, and theprocessor can vary the ablative energy in response to an anteriorconical radius of curvature signal. The tissue will typically include aconical tissue of an eye, and the delivery system may include an opticaldelivery system transmitting photoablative laser energy toward theconical tissue so as to selectively alter an optical characteristic ofthe eye. The processor may vary a quantity of change in the opticalcharacteristic of the eye in response to the anterior corneal radius ofcurvature signal. For example, the processor may vary a diopter value ofthe resculpting procedure in response to the anterior corneal radius ofcurvature. Alternatively, the processor may vary the shape of theablation by altering the ablative energy pattern so as to compensate forlocal differences in anterior corneal radius of curvature across thetarget region of the corneal tissue. In some embodiments, an outputdevice coupled to the processor may show a display in response to theanterior corneal radius of curvature signal.

Systems and methods for sculpting of a corneal tissue of an eye toeffect a desired change in an optical property are also provided herein.Such techniques can include sensing or detecting an anterior cornealradius of curvature, and determining a desired change in shape of theeye in response to the anterior corneal radius of curvature, and inresponse to the desired change in optical property. A pattern of laserenergy can be planned for directing toward the corneal tissue, so at toeffect the determined change in shape. A desired change in opticalquality can be determined while the tissue has a initial anteriorcorneal radius of curvature, or a subsequent anterior corneal radius ofcurvature following or during an ablation or resculpting step. Thechange in optical quality may be determined using any of a variety ofstandard vision diagnostic systems. Wavefront sensor systems now beingdeveloped may also be beneficial for determining a desired change in anoptical property, and still further alternative topography and/ortomography systems may also be used. Regardless, rather than simplydetermining the desired change in shape of the eye from suchmeasurements alone, the desired sculpting or ablation shape can also bebased in part on the anterior corneal radius of curvature.

An exemplary method for performing an anterior corneal radius ofcurvature compensated photorefractive ablation may be initiated using apredetermined ablation pattern assuming a standard ablation rate. Asensor can be used to determine or evaluate the anterior corneal radiusof curvature. The standard ablation rate can be adjusted based on theanterior conical radius of curvature, and the adjusted ablation rate canbe part of a treatment pattern of ablation energy directed toward thetissue so as to effect the desired change in optical characteristics ofeye. The treatment pattern, can include parameters such as the size,location, and/or number of laser pulses directed toward some or all ofthe treatment region of the eye. One or more of these parameters can beset or adjusted based on the anterior corneal radius of curvature. Insome cases, an algorithm used to calculate a shot pattern so as toeffect a desired change in corneal shape may incorporate adjustedablation rates appropriate for a varying anterior corneal radius ofcurvature.

Embodiments of the present invention may involve fine-tuning techniquesthat incorporate wavefront and topographic features of an opticalsystem. Exemplary approaches for determining shapes and features of thetopography of a corneal of the eye are discussed in, for example, U.S.patent application Ser. Nos. 11/769,054 and 12/119,293 filed Jun. 27,2007 and May 12, 2008, respectively, which are incorporated herein byreference for all purposes.

Compensation of Corneal Biomechanics and Healing

Techniques that involve cutting a flap with a microkeratome may cause achange of the high order aberrations. In some laser ablations, anincrease of the high order aberrations can be dominated by the sphericalaberrations. In general, when the pre-operative high order root meansquare (RMS) error of the aberrations is low, ocular aberrations cantend to increase after surgery. On the other hand, when thepre-operative high order RMS error is high, ocular aberrations can tendto decrease. The increase of the spherical aberration post-surgery maynot be all due to the biomechanics and healing, neglect of some of theeffects discussed in this section may also cause an increase inspherical aberrations.

To compensate for the induction of ocular aberrations due tobiomechanics and healing, mechanical and optical models have beenproposed. For example, one way to account for the induction of ocularaberrations is to treat the biomechanical and healing effects as a lowpass filtering process. When a flap is laid onto an ablated structure,some of the sharper, or higher spatial frequency, features can besmoothed. Similarly, when the ablated cornea heals, some of the smallerstructures, whether it is due to the flap cut or due to the gaps betweenthe laser pulses, can also be smoothed out.

Another approach, which can be useful in addressing the effect of a flapcut, for example, is to use mechanical models. Before the LASIK flap iscut, the tension of the lamellae is maintained between the interlamellarcrosslinking, and the corneal internal fluid and intraocular pressures.After the flap is cut, the lamellar segments at the edge of the cut losethe tension, hence making the peripheral cornea to expand. This in turncan increase the interlamellar spacing, causing the edge of the cut tobulge and the central ablation area to flatten. After the flap is putback, the lost tension at the edge of the flap may not be able torecover. Therefore, the deformation of the cornea due to the flap cutmay remain. Optically, this can create a phase advance at the center ofthe cut and a phase lag at the periphery, or the induction of a positivespherical aberration. With modeling, such as with finite element method,for example, a prediction of the corneal surface deformation after flapcut is possible.

Determination of Treatment Shape

In some embodiments, systems and methods may involve producing atreatment shape in a variety of steps. For example, an optical regionshape can be determined, either by Munnerlyn equations or wavefronttechniques. In some cases, aspects of the shape can be smoothed by pixelaveraging, or by spatial averaging of depth.

Once the desired ablation shape has been determined, a next step is todefine the parameters of the actual laser ablation required toadminister the treatment ablation profile. A particularly useful way ofdetermining these parameters is by using an ablation equation, such asthe one shown below.

${AblationShape} = {\sum\limits_{n = 1}^{TotalPulses}( {{PulseShape}_{n} \otimes {Position}_{n}} )}$

In brief, this equation is based on the principle that a treatmentablation is the sum of each of the individual laser pulses. Thisequation has been empirically verified on a variety of materialsincluding plastic, and bovine, porcine, and human corneal tissue.

In this equation, the AblationShape variable represents the desiredablation shape. In this sense, it is a known variable. The target shapecan be, for example, a simple sphere, an ellipse, a cylinder fortreating myopia or hyperopia, or even a saddle for treating mixedastigmatism. The target shape can be any arbitrary shape, such as themap from a wavefront type device or any other topography system.

The PulseShape variable, which is also a known variable, represents theablation shape of each laser pulse size to be used. The PulseShapetypically varies for different ablated materials, such as plastic,animal cornea, or human cornea. The PulseShape also typically varies foreach laser pulse diameter. An example of this type of ablation data isshown in FIG. 5. This figure shows different shapes of craters expectedfrom a single laser pulse. There is a unique description for everyunique pulse shape or size to be used. By systematically measuring theshape which each laser pulse ablates onto a specific target material, itis possible to generate such basis data for a variety of materials, suchas tissue or plastic. For a given material, at a given diameter, theshape is generally consistent from laser system to laser system.

A fixed spot laser may have only one description, while a variable spotlaser could have as many as desired. There is no requirement that thecrater shape be flat, round, or symmetric. As long as it can bedescribed mathematically or with an array of data, it can beincorporated in the equation.

In order to create the ablated surface, it is useful to determine thelocations where each of the laser pulses will be applied. The Positionvariable, which represents the exact position of every laser pulse, isan unknown variable. This variable is calculated by solving the ablationequation. Put another way, the output is a set of instructions forcreating the target ablation shape using the laser pulses. This issometimes called a treatment table. The treatment table consists of alist of individual pulses, each containing the size and offset, orposition, to be used for that pulse. When the laser fires according tothe instructions in the treatment table, the target shape will becreated.

The target ablation shape is a theoretical construct; it is amathematically perfect representation of a desired ablation outcome. Putanother way, while the application of thousands of specifically placedbrief laser pulses can create an actual ablation shape that approachesthe ideal target ablation shape, in the end it is still an approximationthereof.

Therefore, solving for the Position variable can allow for theformulation of a corresponding ablation shape that approaches the targetablation shape as closely as possible. In this way each of the thousandsof pulse positions are individually determined so as to minimize thedifference between the ideal target ablation shape and the actualresulting ablation shape. In a system for ablating tissue using ascanning laser, a presently preferred computational technique forachieving this goal employs simulated annealing.

Other mathematical approaches include, for example, the SALSA Algorithm.SALSA is an acronym for Simulated Annealing Least Squares Algorithm. Itis an algorithm that solves an equation having over 10,000 unknowns. Thealgorithm finds the best solution by selecting: the number of pulses,the size of each pulse, and the location of each pulse. It is an exactalgorithm, and makes no statistical assumptions.

Simulated Annealing is a recent, proven method to solve otherwiseintractable problems, and may be used to solve the ablation equationdiscussed above. This is more fully described in PCT Application No.PCT/US01/08337, filed Mar. 14, 2001, the entire disclose of which isincorporated herein by reference. See also W. H. Press et al.,“Numerical Recipes in C” 2^(nd) Ed., Cambridge University Press, pp.444-455 (1992). This approach is also further discussed in co-pendingU.S. patent application Ser. No. 09/805,737, the entire disclosure ofwhich is incorporated herein by reference.

Simulated annealing is a method used for minimizing (or maximizing) theparameters of a function. It is particularly suited to problems withvery large, poorly behaved function spaces. Simulated annealing can beapplied in the same way regardless of how many dimensions are present inthe search space. It can be used to optimize any conditions that can beexpressed numerically, and it does not require a derivative. It can alsoprovide an accurate overall minimum despite local minima in the searchspace, for example.

The methods and apparatuses of the present invention may be provided inone or more kits for such use. The kits may comprise a system forprofiling an optical surface, such as an optical surface of an eye, andinstructions for use. Optionally, such kits may further include any ofthe other system components described in relation to the presentinvention and any other materials or items relevant to the presentinvention. The instructions for use can set forth any of the methods asdescribed above.

Each of the above calculations or operations may be performed using acomputer or other processor having hardware, software, and/or firmware.The various method steps may be performed by modules, and the modulesmay comprise any of a wide variety of digital and/or analog dataprocessing hardware and/or software arranged to perform the method stepsdescribed herein. The modules optionally comprising data processinghardware adapted to perform one or more of these steps by havingappropriate machine programming code associated therewith, the modulesfor two or more steps (or portions of two or more steps) beingintegrated into a single processor board or separated into differentprocessor boards in any of a wide variety of integrated and/ordistributed processing architectures. These methods and systems willoften employ a tangible media embodying machine-readable code withinstructions for performing the method steps described above. Suitabletangible media may comprise a memory (including a volatile memory and/ora non-volatile memory), a storage media (such as a magnetic recording ona floppy disk, a hard disk, a tape, or the like; on an optical memorysuch as a CD, a CD-R/W, a CD-ROM, a DVD, or the like; or any otherdigital or analog storage media), or the like.

All patents, patent publications, patent applications, journal articles,books, technical references, and the like discussed in the instantdisclosure are incorporated herein by reference in their entirety forall purposes.

While the above provides a full and complete disclosure of the preferredembodiments of the present invention, various modifications, alternateconstructions and equivalents may be employed as desired. Therefore, theabove description and illustrations should not be construed as limitingthe invention, which can be defined by the appended claims.

1-5. (canceled)
 6. A system for determining a refractive treatment shapefor an eye of a patient, the system comprising: an input configured toreceive a variable radius of curvature of an anterior surface of acornea of the eye; and a processing module comprising a tangible mediumembodying machine-readable code that determines the refractive treatmentshape for the eye based on the variable radius of curvature of theanterior surface.
 7. The system according to claim 6, further comprisingan ablation system configured to apply the refractive treatment shape tothe patient.
 8. The system according to claim 6, wherein the variableradius of curvature of the anterior surface of the eye is a function ofa radius of curvature of a posterior surface of the cornea.
 9. Thesystem according to claim 6, where in the variable radius of curvatureof the anterior surface of the eye varies as a function of an ablationdepth. 10-22. (canceled)
 23. A method of determining a refractivetreatment shape for an eye of a patient, the method comprising:determining a variable radius of curvature of an anterior surface of acornea of the eye; and determining the refractive treatment shape forthe eye based on the variable radius of curvature.
 24. The methodaccording to claim 23, wherein determining the refractive treatmentshape comprises determining a refractive treatment shape of a remainingablation for the eye based on the variable radius of curvature.
 25. Themethod according to claim 23, wherein the variable radius of curvaturefor the cornea of the eye is determined following application of one ormore ablation pulses to the eye.
 26. The method according to claim 23,further comprising applying the refractive treatment shape to the eyewith an ablation system.
 27. The method according to claim 23, whereinthe variable radius of curvature of the anterior surface of the eyevaries as a function of cornea thickness.
 28. The method according toclaim 23, wherein the variable radius of curvature of the anteriorsurface of the eye is a function of a radius of curvature of a posteriorsurface of the cornea.
 29. The method according to claim 23, wherein thevariable radius of curvature of the anterior surface of the eye variesas a function of an ablation depth.
 30. The method according to claim23, wherein the refractive treatment shape for the eye is based on aMunnerlyn equation.